Suppose the number of general aviation aircraft accidents from 1975 through 1997 can be modeled by accidents where x is the number of years since 1975. Use a definite integral to estimate, to the nearest accident, the number of accidents that occurred each year from 1978 through 1994.
A) 37,560 accidents
B) 3,509 accidents
C) 2,861 accidents
D) 3,577 accidents
E) 1,754 accidents

Question

Suppose the number of general aviation aircraft accidents from 1975 through 1997 can be modeled by  accidents where x is the number of years since 1975. Use a definite integral to estimate, to the nearest accident, the number of accidents that occurred each year from 1978 through 1994.
A) 37,560 accidents 
B) 3,509 accidents 
C) 2,861 accidents 
D) 3,577 accidents 
E) 1,754 accidents

Quizplus · Accepted Answer

To estimate the number of accidents that occurred each year from 1978 to 1994, we need to evaluate the definite integral of the given model function from x = 3 (1978-1975) to x = 19 (1994-1975), then divide by the number of years:

(1/16) ∫_(x=3)^(x=19) 11e^(0.221x) dx

Using a calculator or integration software, this evaluates to approximately 2861 accidents per year. Therefore, the answer is C.

Suppose the Number of General Aviation Aircraft Accidents from 1975